FORECASTING USING R Welcome to Forecasting Using R Rob Hyndman Author, forecast
Forecasting Using R What you will learn ● Exploring and visualizing time series ● Simple benchmark methods for forecasting ● Exponential smoothing and ARIMA models ● Advanced forecasting methods ● Measuring forecast accuracy ● Choosing the best method
Forecasting Using R Course textbook Hyndman, R. J. & Athanasopoulos, G. (2017) Forecasting: principles and practice , 2nd edition ● Free and online at OTexts.org/fpp2/ ● Data sets in associated R package fpp2 ● R code for all examples
Forecasting Using R Time series data ● Series of data observed over time ● Eg.: Daily IBM stock prices, monthly rainfall in London,… Forecasting is estimating how the sequence of observations will continue into the future.
Forecasting Using R Forecasts of monthly Australian expenditure on eating out ● What forecasting methods are available that take account of trend, seasonality and other features of the data? ● How to measure the accuracy of your forecasts? ● How to choose a good forecasting model?
FORECASTING USING R Let’s practice!
FORECASTING USING R Trends, seasonality, and cyclicity
Forecasting Using R Time series pa � erns Pa � ern Description A pa � ern exists involving a long-term increase OR decrease in Trend the data A periodic pa � ern exists due to the calendar Seasonal (e.g. the quarter, month, or day of the week) A pa � ern exists where the data exhibits rises and falls that are Cyclic not of fixed period (duration usually of at least 2 years)
Forecasting Using R Examples of time series pa � erns
Forecasting Using R Examples of time series pa � erns
Forecasting Using R Examples of time series pa � erns
Forecasting Using R Examples of time series pa � erns
Forecasting Using R Seasonal or cyclic? Di ff erences between seasonal and cyclic pa � erns: Seasonal pa � ern constant length vs. cyclic pa � ern variable ● length Average length of cycle longer than length of seasonal pa � ern ● ● Magnitude of cycle more variable than magnitude of seasonal pa � ern The timing of peaks and troughs is predictable with seasonal data, but unpredictable in the long term with cyclic data.
FORECASTING USING R Let’s practice!
FORECASTING USING R White noise
Forecasting Using R White noise > set.seed(3) # Reproducibility > wn <- ts(rnorm(36)) # White noise > autoplot(wn) # Plot! "White noise" is just a time series of iid data
Forecasting Using R White noise ACF > ggAcf(wn) + ggtitle("Sample ACF for white noise") Expectation: each autocorrelation is close to zero 95% of all autocorrelations for white If not: series is probably noise should lie within the blue lines not white noise
Forecasting Using R Example: Pigs slaughtered > autoplot(pigs/1000) + > xlab("Year") + > ylab("thousands") + > ggtitle("Monthly number of pigs slaughtered in Victoria")
Forecasting Using R Example: Pigs slaughtered > ggAcf(pigs) + > ggtitle("ACF of monthly pigs slaughtered in Victoria") significant autocorrelation at lags 1, 2, and 3 Not a white noise series: there is info in the data that can be used to forecast future values
Forecasting Using R Ljung-Box test The Ljung-Box test considers the first h autocorrelation values together . A significant test (small p-value) indicates the data are probably not white noise. > Box.test(pigs, lag = 24, fitdf = 0, type = "Lj") Box-Ljung test data: pigs X-squared = 634.15, df = 24, p-value < 2.2e-16
Forecasting Using R White noise summary ● White noise is a time series that is purely random ● We can test for white noise by looking at an ACF plot or by doing a Ljung-Box test
FORECASTING USING R Let’s practice!
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